Collapse of $\rho_{xx}$ ringlike structures in 2DEGs under tilted magnetic fields

TL;DR

This paper models the collapse of ringlike structures in the longitudinal resistivity of 2DEGs under tilted magnetic fields, revealing that inter Landau-level coupling causes these structures to shrink and collapse at a critical tilt angle.

Contribution

It introduces a non-interacting theoretical model accounting for Landau-level anti-crossings to explain the collapse of ringlike structures in 2DEGs under tilted magnetic fields.

Findings

Ring structures shrink with increasing tilt angle

Collapse occurs at approximately 3.6 degrees in the model

The model captures the essential mechanism of ring collapse

Abstract

In the quantum Hall regime, the longitudinal resistivity $\rho_{xx}$ plotted as a density--magnetic-field ($n_{2D}-B$) diagram displays ringlike structures due to the crossings of two sets of spin split Landau levels from different subbands [e.g., Zhang \textit{et al.}, Phys. Rev. Lett. \textbf{95}, 216801 (2005)]. For tilted magnetic fields, some of these ringlike structures "shrink" as the tilt angle is increased and fully collapse at $\theta_c \approx 6^\circ$. Here we theoretically investigate the topology of these structures via a non-interacting model for the 2DEG. We account for the inter Landau-level coupling induced by the tilted magnetic field via perturbation theory. This coupling results in anti-crossings of Landau levels with parallel spins. With the new energy spectrum, we calculate the corresponding $n_{2D}-B$ diagram of the density of states (DOS) near the Fermi level. We argue that the DOS displays the same topology as $\rho_{xx}$ in the $n_{2D}-B$ diagram. For the ring with filling factor $\nu=4$, we find that the anti-crossings make it shrink for increasing tilt angles and collapse at a large enough angle. Using effective parameters to fit the $\theta = 0^\circ$ data, we find a collapsing angle $\theta_c \approx 3.6^\circ$. Despite this factor-of-two discrepancy with the experimental data, our model captures the essential mechanism underlying the ring collapse.